Simulation of axisymmetric free surface viscous flow around a non-spherical bubble in the sonoluminescence regime

Overview & Synopsis

When excited with ultrasound waves, air bubbles in water can, in appropriate con ditions, emit light. This phenomenon is known as {\em sonoluminescence}. While recent experiments have successfully produced stable single bubble sonolum inescence, allowing the conditions for sonoluminescence to be studied in more de tail, the mechanism for light emission remains little understood. The classical explanation relies on a shock wave theory \cite{crum94}\cite{greenspan93}. These authors suggest th at during the violent collapse of the bubble, spherical shock waves are emitted which concentrate on a singular point at the center of the bubble yielding very high temperatures ($>$ 10,000 {\kelvin}) and very short light pulses ($\approx$ 50 picoseconds)\ci te{barber91}. However, this hypothesis has serious weak points underlined by A. Prosperetti \cite{prosp eretti97}. The main assumption of the shock wave hypothesis is that the bubble remains spherical throughout the pressure cycle. There is strong evidence that the bubble should deform strongly when reaching very small radii. In particular a jet of liquid should form in the direction of the bubble motion. If this is the case, the shock wave model does not hold anymore (at least in its present form) and another mechanism for light emission should be found. Our goal is to illustrate numerically the possibility of stable and repeatable formation of a jet at each sonoluminescence cycle. While some boundary-integral computations have been made \cite{prosperetti97}, we are not aware of a full Navier-Stokes simulation o f such a phenomenon. The phenomenon of jet formation is moreover a characteristic of cavitation bubbl es near solid walls. Sonoluminescence and cavitation thus appear to be closely r elated \cite{Lauterborn97}. We will present a free-surface Navier-Stokes solver which can be useful for the study of these two phenomena and some results regarding both cavitation and sono luminescence.